Finite Group Databasebeta

← C7×#15163 #13192379

Subgroups — C7×#15163 #13192379

Order 1792.

1862 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#398C211yesmaximal, characteristic, complemented
2C2×C7×#396C212yesmaximal, complemented
3C2×C7×#394C211yesmaximal, characteristic
4C2×C7×#390C211yesmaximal, characteristic
5C2×C7×#388C212yesmaximal, complemented
6C2×C4×C7×C4⋊C4C211yesmaximal, characteristic, complemented
7C7×#1445C211yesmaximal, characteristic, complemented
8C7×#1439C212yesmaximal, complemented
9C7×#1438C211yesmaximal, characteristic
10C7×#1437C212yesmaximal, complemented
11C7×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C7×D4C2211yescharacteristic
13C22×C7×C4⋊C4C2212yes—
14C22×C7×C4⋊C4C2211yescharacteristic
15C22×C7×C4⋊C4C2212yes—
16C22×C7×C4⋊C4C2211yescharacteristic
17C22×C7×C4⋊C4C2211yescharacteristic
18C22×C7×C22⋊C4C2212yes—
19C22×C7×C22⋊C4C2212yes—
20C22×C7×C22⋊C4C2212yes—
21C22×C7×C22⋊C4C2212yes—
22C22×C7×C22⋊C4C2212yes—
23C22×C7×C22⋊C4C2212yes—
24C22×C42×C7C2211yescharacteristic
25C22×C42×C7C2211yescharacteristic
26C22×C42×C7C2211yescharacteristic
27C7×#398—24no—
28C7×#396—28no—
29C7×#394—24no—
30C7×#390—24no—
31C7×#388—28no—
32C4×C7×C4⋊C4—24no—
33C2×C7×#95C2212yes—
34C2×C7×#95C2211yescharacteristic
35C2×C7×#95C2212yes—
36C2×C7×#95C2211yescharacteristic
37C2×C7×#95C2211yescharacteristic
38C2×C7×#95C2212yes—
39C2×C7×#95C2212yes—
40C2×C7×#95C2211yescharacteristic
41#15163C711yesmaximal, characteristic, direct product factor, Sylow
42C25×C7C2312yes—
43C22×C7×D4—24no—
44C22×C7×D4—22no—
45C22×C7×D4—22no—
46C22×C7×D4—22no—
47C22×C7×D4—42no—
48C23×C4×C7C2312yes—
49C23×C4×C7C2312yes—
50C23×C4×C7C2311yescharacteristic
51C23×C4×C7C2311yescharacteristic
52C23×C4×C7C2311yescharacteristic
53C23×C4×C7C2312yes—
54C23×C4×C7C2311yescharacteristic
55C23×C4×C7C2311yescharacteristic
56C23×C4×C7C2311yescharacteristic
57C23×C4×C7C2311yescharacteristic
58C2×C7×C4⋊C4—22no—
59C2×C7×C4⋊C4—22no—
60C2×C7×C4⋊C4—22no—
61C2×C7×C4⋊C4—22no—
62C2×C7×C4⋊C4—24no—
63C2×C7×C4⋊C4—22no—
64C2×C7×C4⋊C4—24no—
65C2×C7×C4⋊C4—24no—
66C2×C7×C4⋊C4—22no—
67C2×C7×C4⋊C4—24no—
68C2×C7×C4⋊C4—24no—
69C2×C7×C4⋊C4—22no—
70C2×C7×C4⋊C4—42no—
71C2×C7×C4⋊C4D414yes—
72C2×C7×C4⋊C4D414yescomplemented
73C2×C7×C22⋊C4—24no—
74C2×C7×C22⋊C4—24no—
75C2×C7×C22⋊C4—24no—
76C2×C7×C22⋊C4—24no—
77C2×C7×C22⋊C4—24no—
78C2×C7×C22⋊C4—24no—
79C2×C7×C22⋊C4—24no—
80C2×C7×C22⋊C4—24no—
81C2×C7×C22⋊C4—24no—
82C2×C7×C22⋊C4—24no—
83C2×C7×C22⋊C4—24no—
84C2×C7×C22⋊C4—24no—
85C2×C7×C22⋊C4—24no—
86C2×C7×C22⋊C4—24no—
87C2×C7×C22⋊C4—24no—
88C2×C7×C22⋊C4—24no—
89C2×C7×C22⋊C4—42no—
90C2×C7×C22⋊C4—42no—
91C2×C42×C7—22no—
92C2×C42×C7—22no—
93C2×C42×C7—22no—
94C2×C42×C7—42no—
95C2×C42×C7—42no—
96C2×C42×C7D414yes—
97C2×C42×C7D414yescomplemented
98C7×#95—22no—
99C7×#95—22no—
100C7×#95—24no—
101C7×#95—24no—
102C7×#95—22no—
103C7×#95—24no—
104C7×#95—22no—
105C7×#95—24no—
106C2×#398C2×C711yescharacteristic, complemented
107C2×#396C2×C712yescomplemented
108C2×#394C2×C711yescharacteristic
109C2×#390C2×C711yescharacteristic
110C2×#388C2×C712yescomplemented
111C2×C4×C4⋊C4C2×C711yescharacteristic, complemented
112#1445C2×C711yescharacteristic, complemented
113#1439C2×C712yescomplemented
114#1438C2×C711yescharacteristic
115#1437C2×C712yescomplemented
116C4⋊#95C2×C711yescharacteristic, complemented
117C24×C7—22no—
118C24×C7—22no—
119C24×C7—22no—
120C24×C7—22no—
121C24×C7—22no—
122C24×C7—22no—
123C24×C7—22no—
124C24×C7—22no—
125C24×C7—22no—
126C24×C7—22no—
127C24×C7—22no—
128C24×C7—22no—
129C24×C7—22no—
130C24×C7—22no—
131C24×C7#4114yes—
132C24×C7C2411yescharacteristic
133C2×C7×D4—28no—
134C2×C7×D4—48no—
135C2×C7×D4—48no—
136C2×C7×D4—44no—
137C2×C7×D4—44no—
138C22×C4×C7—21no—
139C22×C4×C7—21no—
140C22×C4×C7—21no—
141C22×C4×C7—21no—
142C22×C4×C7—22no—
143C22×C4×C7—22no—
144C22×C4×C7—22no—
145C22×C4×C7—22no—
146C22×C4×C7—22no—
147C22×C4×C7—22no—
148C22×C4×C7—21no—
149C22×C4×C7—22no—
150C22×C4×C7—21no—
151C22×C4×C7—21no—
152C22×C4×C7—22no—
153C22×C4×C7—22no—
154C22×C4×C7—21no—
155C22×C4×C7—22no—
156C22×C4×C7—22no—
157C22×C4×C7—22no—
158C22×C4×C7—22no—
159C22×C4×C7—22no—
160C22×C4×C7—21no—
161C22×C4×C7—21no—
162C22×C4×C7—22no—
163C22×C4×C7—22no—
164C22×C4×C7—22no—
165C22×C4×C7—22no—
166C22×C4×C7—22no—
167C22×C4×C7—22no—
168C22×C4×C7—22no—
169C22×C4×C7—22no—
170C22×C4×C7—22no—
171C22×C4×C7—22no—
172C22×C4×C7—22no—
173C22×C4×C7—22no—
174C22×C4×C7—22no—
175C22×C4×C7—22no—
176C22×C4×C7—22no—
177C22×C4×C7—22no—
178C22×C4×C7—22no—
179C22×C4×C7—22no—
180C22×C4×C7C2×D412yes—
181C22×C4×C7C2×D412yes—
182C22×C4×C7C2×D412yes—
183C22×C4×C7C2×D412yes—
184C22×C4×C7C2×D412yes—
185C22×C4×C7C2×D412yes—
186C22×C4×C7C2×D412yes—
187C22×C4×C7C2×D412yes—
188C22×C4×C7C2×D412yes—
189C22×C4×C7C2×D412yes—
190C22×C4×C7C2×D412yes—
191C22×C4×C7C2×D412yes—
192C22×C4×C7#4114yes—
193C22×C4×C7#4112yes—
194C22×C4×C7#4112yes—
195C22×C4×C7#4112yes—
196C7×C4⋊C4—28no—
197C7×C4⋊C4—28no—
198C7×C4⋊C4—48no—
199C7×C4⋊C4—44no—
200C7×C4⋊C4—48no—
201C7×C22⋊C4—216no—
202C7×C22⋊C4—48no—
203C7×C22⋊C4—48no—
204C7×C22⋊C4—48no—
205C7×C22⋊C4—48no—
206C7×C22⋊C4—48no—
207C42×C7—28no—
208C42×C7—44no—
209C42×C7—44no—
210C23×D4C22×C711yescharacteristic
211C22×C4⋊C4C22×C712yes—
212C22×C4⋊C4C22×C711yescharacteristic
213C22×C4⋊C4C22×C712yes—
214C22×C4⋊C4C22×C711yescharacteristic
215C22×C4⋊C4C22×C711yescharacteristic
216C22×C22⋊C4C22×C712yes—
217C22×C22⋊C4C22×C712yes—
218C22×C22⋊C4C22×C712yes—
219C22×C22⋊C4C22×C712yes—
220C22×C22⋊C4C22×C712yes—
221C22×C22⋊C4C22×C712yes—
222C22×C42C22×C711yescharacteristic
223C22×C42C22×C711yescharacteristic
224C22×C42C22×C711yescharacteristic
225#398—24no—
226#396—28no—
227#394—24no—
228#390—24no—
229#388—28no—
230C4×C4⋊C4—24no—
231C2×#95C22×C711yescharacteristic
232C2×#95C22×C712yes—
233C2×#95C22×C711yescharacteristic
234C2×#95C22×C712yes—
235C2×#95C22×C712yes—
236C2×#95C22×C711yescharacteristic
237C2×#95C22×C711yescharacteristic
238C2×#95C22×C712yes—
239C23×C7—24no—
240C23×C7—24no—
241C23×C7—24no—
242C23×C7—24no—
243C23×C7—24no—
244C23×C7—24no—
245C23×C7—24no—
246C23×C7—42no—
247C23×C7—42no—
248C23×C7—42no—
249C23×C7—42no—
250C23×C7—42no—
251C23×C7—42no—
252C23×C7—42no—
253C23×C7—42no—
254C23×C7—42no—
255C23×C7—42no—
256C23×C7—42no—
257C23×C7—42no—
258C23×C7—42no—
259C23×C7—42no—
260C23×C7—42no—
261C23×C7—42no—
262C23×C7—42no—
263C23×C7—42no—
264C23×C7—42no—
265C23×C7—42no—
266C23×C7—42no—
267C23×C7—42no—
268C23×C7—42no—
269C23×C7—42no—
270C23×C7—42no—
271C23×C7—42no—
272C23×C7—42no—
273C23×C7—42no—
274C23×C7C22×D411yescharacteristic
275C23×C7C22×D411yescharacteristic
276C23×C7C22×D411yescharacteristic
277C23×C7C22×D411yescharacteristic
278C23×C7C2×#4111yescharacteristic
279C23×C7C2×#4111yescharacteristic
280C23×C7C2×#4111yescharacteristic
281C23×C7C2×#4112yes—
282C23×C7C2×#4112yes—
283C23×C7H(5,𝔽2)12yes—
284C23×C72−1+412yes—
285C7×D4—416no—
286C2×C4×C7—22no—
287C2×C4×C7—22no—
288C2×C4×C7—22no—
289C2×C4×C7—22no—
290C2×C4×C7—22no—
291C2×C4×C7—22no—
292C2×C4×C7—22no—
293C2×C4×C7—22no—
294C2×C4×C7—22no—
295C2×C4×C7—22no—
296C2×C4×C7—22no—
297C2×C4×C7—22no—
298C2×C4×C7—24no—
299C2×C4×C7—24no—
300C2×C4×C7—24no—
301C2×C4×C7—24no—
302C2×C4×C7—24no—
303C2×C4×C7—24no—
304C2×C4×C7—22no—
305C2×C4×C7—22no—
306C2×C4×C7—22no—
307C2×C4×C7—24no—
308C2×C4×C7—24no—
309C2×C4×C7—24no—
310C2×C4×C7—24no—
311C2×C4×C7—24no—
312C2×C4×C7—24no—
313C2×C4×C7—41no—
314C2×C4×C7—41no—
315C2×C4×C7—42no—
316C2×C4×C7—42no—
317C2×C4×C7—41no—
318C2×C4×C7—41no—
319C2×C4×C7—41no—
320C2×C4×C7—41no—
321C2×C4×C7—42no—
322C2×C4×C7—42no—
323C2×C4×C7—42no—
324C2×C4×C7—42no—
325C2×C4×C7—42no—
326C2×C4×C7—42no—
327C2×C4×C7—42no—
328C2×C4×C7—42no—
329C2×C4×C7—42no—
330C2×C4×C7—42no—
331C2×C4×C7—42no—
332C2×C4×C7—42no—
333C2×C4×C7—42no—
334C2×C4×C7—42no—
335C2×C4×C7—42no—
336C2×C4×C7—42no—
337C2×C4×C7—42no—
338C2×C4×C7—42no—
339C2×C4×C7—42no—
340C2×C4×C7#12114yes—
341C2×C4×C7#12114yes—
342C2×C4×C7#12114yes—
343C2×C4×C7#12714yes—
344C25C23×C712yes—
345C22×D4—24no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—42no—
350C23×C4C23×C712yes—
351C23×C4C23×C712yes—
352C23×C4C23×C711yescharacteristic
353C23×C4C23×C711yescharacteristic
354C23×C4C23×C711yescharacteristic
355C23×C4C23×C712yes—
356C23×C4C23×C711yescharacteristic
357C23×C4C23×C711yescharacteristic
358C23×C4C23×C711yescharacteristic
359C23×C4C23×C711yescharacteristic
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4C7×D414yes—
374C2×C4⋊C4C7×D414yescomplemented
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42C7×D414yes—
399C2×C42C7×D414yescomplemented
400#95—22no—
401#95—22no—
402#95—24no—
403#95—24no—
404#95—22no—
405#95—24no—
406#95—22no—
407#95—24no—
408C22×C7—44no—
409C22×C7—44no—
410C22×C7—44no—
411C22×C7—44no—
412C22×C7—44no—
413C22×C7—44no—
414C22×C7—44no—
415C22×C7—82no—
416C22×C7—82no—
417C22×C7—82no—
418C22×C7—82no—
419C22×C7—82no—
420C22×C7—82no—
421C22×C7—82no—
422C22×C7—82no—
423C22×C7C2×#12111yescharacteristic
424C22×C7C2×#12111yescharacteristic
425C22×C7C2×#12111yescharacteristic
426C22×C7#52512yes—
427C22×C7#52511yescharacteristic
428C22×C7#52912yes—
429C22×C7C2×#12711yescharacteristic
430C22×C7#53211yescharacteristic
431C22×C7#53211yescharacteristic
432C22×C7#53211yescharacteristic
433C22×C7#53211yescharacteristic
434C22×C7#53411yescharacteristic
435C22×C7#53611yescharacteristic
436C22×C7#53712yes—
437C22×C7#53912yes—
438C22×C7#54612yes—
439C22×C7#54612yes—
440C22×C7#54812yes—
441C22×C7#54812yes—
442C22×C7#55112yes—
443C22×C7#55212yes—
444C22×C7#55312yes—
445C22×C7#55612yes—
446C4×C7—24no—
447C4×C7—24no—
448C4×C7—24no—
449C4×C7—24no—
450C4×C7—42no—
451C4×C7—42no—
452C4×C7—44no—
453C4×C7—42no—
454C4×C7—82no—
455C4×C7—82no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24C7×#4114yes—
471C24C24×C711yescharacteristic
472C2×D4—28no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—44no—
476C2×D4—44no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4C2×C7×D412yes—
520C22×C4C2×C7×D412yes—
521C22×C4C2×C7×D412yes—
522C22×C4C2×C7×D412yes—
523C22×C4C2×C7×D412yes—
524C22×C4C2×C7×D412yes—
525C22×C4C2×C7×D412yes—
526C22×C4C2×C7×D412yes—
527C22×C4C2×C7×D412yes—
528C22×C4C2×C7×D412yes—
529C22×C4C2×C7×D412yes—
530C22×C4C2×C7×D412yes—
531C22×C4C7×#4114yes—
532C22×C4C7×#4112yes—
533C22×C4C7×#4112yes—
534C22×C4C7×#4112yes—
535C4⋊C4—28no—
536C4⋊C4—28no—
537C4⋊C4—48no—
538C4⋊C4—44no—
539C4⋊C4—48no—
540C22⋊C4—216no—
541C22⋊C4—48no—
542C22⋊C4—48no—
543C22⋊C4—48no—
544C22⋊C4—48no—
545C22⋊C4—48no—
546C42—28no—
547C42—44no—
548C42—44no—
549C2×C7—84no—
550C2×C7#239211yescharacteristic
551C2×C7#253411yescharacteristic
552C2×C7#253611yescharacteristic
553C2×C7#254012yes—
554C2×C7#254311yescharacteristic
555C2×C7#254511yescharacteristic
556C2×C7#255812yes—
557C2×C7#256012yes—
558C2×C7#260112yes—
559C2×C7#261811yescharacteristic
560C2×C7#285611yescharacteristic
561C23—24no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23C22×C7×D411yescharacteristic
597C23C22×C7×D411yescharacteristic
598C23C22×C7×D411yescharacteristic
599C23C22×C7×D411yescharacteristic
600C23C2×C7×#4111yescharacteristic
601C23C2×C7×#4111yescharacteristic
602C23C2×C7×#4111yescharacteristic
603C23C2×C7×#4112yes—
604C23C2×C7×#4112yes—
605C23C7×H(5,𝔽2)12yes—
606C23C7×2−1+412yes—
607D4—416no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4C7×#12114yes—
663C2×C4C7×#12114yes—
664C2×C4C7×#12114yes—
665C2×C4C7×#12714yes—
666C7#1516311yescharacteristic, direct product factor, Sylow
667C22—44no—
668C22—44no—
669C22—44no—
670C22—44no—
671C22—44no—
672C22—44no—
673C22—44no—
674C22—82no—
675C22—82no—
676C22—82no—
677C22—82no—
678C22—82no—
679C22—82no—
680C22—82no—
681C22—82no—
682C22C2×C7×#12111yescharacteristic
683C22C2×C7×#12111yescharacteristic
684C22C2×C7×#12111yescharacteristic
685C22C7×#52511yescharacteristic
686C22C7×#52512yes—
687C22C7×#52912yes—
688C22C2×C7×#12711yescharacteristic
689C22C7×#53211yescharacteristic
690C22C7×#53211yescharacteristic
691C22C7×#53211yescharacteristic
692C22C7×#53211yescharacteristic
693C22C7×#53411yescharacteristic
694C22C7×#53611yescharacteristic
695C22C7×#53712yes—
696C22C7×#53912yes—
697C22C7×#54612yes—
698C22C7×#54612yes—
699C22C7×#54812yes—
700C22C7×#54812yes—
701C22C7×#55112yes—
702C22C7×#55212yes—
703C22C7×#55312yes—
704C22C7×#55612yes—
705C4—24no—
706C4—24no—
707C4—24no—
708C4—24no—
709C4—42no—
710C4—42no—
711C4—44no—
712C4—42no—
713C4—82no—
714C4—82no—
715C2—84no—
716C2C7×#239211yescharacteristic
717C2C7×#253411yescharacteristic
718C2C7×#253611yescharacteristic
719C2C7×#254012yes—
720C2C7×#254311yescharacteristic
721C2C7×#254511yescharacteristic
722C2C7×#255812yes—
723C2C7×#256012yes—
724C2C7×#260112yes—
725C2C7×#261811yescharacteristic
726C2C7×#285611yescharacteristic
subgroupG/H
center, socleC24×C7C24
commutator, Frattini, cosocleC24C24×C7
prime radicalC23×C7×D4C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C7×#398C2semidirect
2. C2×C7×#396C2semidirect
5. C2×C7×#388C2semidirect
6. C2×C4×C7×C4⋊C4C2semidirect
7. C7×#1445C2semidirect
8. C7×#1439C2semidirect
10. C7×#1437C2semidirect
11. C7×C4⋊#95C2semidirect
41. #15163C7direct (N × H)
72. C2×C7×C4⋊C4D4semidirect
97. C2×C42×C7D4semidirect
106. C2×#398C2×C7semidirect
107. C2×#396C2×C7semidirect
110. C2×#388C2×C7semidirect
111. C2×C4×C4⋊C4C2×C7semidirect
112. #1445C2×C7semidirect
113. #1439C2×C7semidirect
115. #1437C2×C7semidirect
116. C4⋊#95C2×C7semidirect
374. C2×C4⋊C4C7×D4semidirect
399. C2×C42C7×D4semidirect
666. C7#15163direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C7×#3982
C2×C7×#3962
C2×C7×#3942
C2×C7×#3902
C2×C7×#3882
C2×C4×C7×C4⋊C42
C7×#14452
C7×#14392
C7×#14382
C7×#14372
C7×C4⋊#952
#151637